#1126 ⟨a, b | ababba=bab⟩

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Properties

Complete rewriting system

Format:
Word to reduce:
Tips:
  • Lowercase letters stand for generators.
  • Spaces are ignored.
  • Numbers repeat the previous letter, e.g. b90.
Reduction strategy:
Path to normal form: 1 
1
  1. a4bc3 ⇒ bc2a
  2. a2b(ca)2 ⇒ cab
  3. a2bcac2 ⇒ c2b
  4. ab2 ⇒ c
  5. bab ⇒ abca
  6. bcb ⇒ abc2
  7. abcab ⇒ bc
  8. bc2ab ⇒ a2bc3
  9. a2bc3b ⇒ bc3
  10. b2c ⇒ ab(ca)2b
  11. bc2bc ⇒ a2bc4ab
  12. a2bcacbc ⇒ c3ab
  13. ba2bca ⇒ abca2b
  14. (bca)2 ⇒ a3bc3
  15. (abca)2 ⇒ bcab
  16. bc2a2bca ⇒ a2bc3ab
  17. a2bc3abca ⇒ bc3ab
  18. ba2bc2 ⇒ abcacb
  19. bcabc2 ⇒ abc3b
  20. abca2bc2 ⇒ bc2b
  21. bc2a2bc2 ⇒ a2bc4b
  22. a2bc3abc2 ⇒ bc4b
  23. ba3bc3 ⇒ abcac2ab
  24. bca2bc3 ⇒ abc4ab
  25. bca3bc3 ⇒ abc3abca
  26. bc2a3bc3 ⇒ a2bc5ab
  27. (a2bc3)2 ⇒ bc5ab
  28. a2bc3a3bc3 ⇒ bc4abca 
# ab:ababba=bab reversed:ac/b abb=c frequency:3/3
aaaabccc=bcca
aabcaca=cab
aabcacc=ccb
abb=c
bab=abca
bcb=abcc
abcab=bc
bccab=aabccc
aabcccb=bccc
bbc=abcacab
bccbc=aabccccab
aabcacbc=cccab
baabca=abcaab
bcabca=aaabccc
abcaabca=bcab
bccaabca=aabcccab
aabcccabca=bcccab
baabcc=abcacb
bcabcc=abcccb
abcaabcc=bccb
bccaabcc=aabccccb
aabcccabcc=bccccb
baaabccc=abcaccab
bcaabccc=abccccab
bcaaabccc=abcccabca
bccaaabccc=aabcccccab
aabcccaabccc=bcccccab
aabcccaaabccc=bccccabca

Right Cayley graph (truncated)

Left Cayley graph (truncated)